Originally posted by Heretic Keklas Rekobah:
</font><blockquote>quote:</font><hr />Originally posted by Space Cadet:
Did you happen to notice that the gamma factors I arrived at for faster than light velocities are imaginary?
No. I noticed that the gamma function is a real-number scalar value with no imaginary component whatsoever. The rest of your explanation is therefore irrelevant.</font>[/QUOTE]Here is my gamma values again. Notice the
i at the end of the gamma values to FTL velocities, this indicates that they are imaginary numbers.
V/c = gamma^2 --------> gamma
0.0001 = 1.00000001 -->1.000000005
0.001 = 1.000001 ----->1.0000005
0.01 = 1.00010001 ---->1.000050004
0.1 = 1.01010101 ----->1.005037815
0.2 = 1.041666667 ---->1.020620726
0.3 = 1.098901099 ---->1.048284837
0.4 = 1.19047619 ----->1.091089451
0.5 = 1.333333333 ---->1.154700538
0.6 = 1.5625 --------->1.25
0.7 = 1.960784314 ---->1.400280084
0.8 = 2.777777778 ---->1.666666667
0.9 = 5.263157895 ---->2.294157339
0.95 = 10.25641026 --->3.202563077
0.98 = 25.25252525 --->5.025189076
0.99 = 50.25125628 --->7.08881205
0.999 = 500.2501251 -->22.36627204
0.9999 = 5,000.250013 ->70.71244596
0.99999 = 50,000.25 -->223.6073568
0.999999 = 500,000 --> 707.1067812
1.000001 = -500,000 -> 707.1067812
i
1.00001 = -49,999.75 -> 223.6062387
i
1.0001 = -4,999.750013 > 70.70891042
i
1.001 = -499.7501249 -> 22.3550917
i
1.01 = -49.75124378 --> 7.053456159
i
1.1 = -4.761904762 ---> 2.182178902
i
1.2 = -2.272727273 ---> 1.507556723
i
1.3 = -1.449275362 ---> 1.203858531
i
1.4 = -1.041666667 ---> 1.020620726
i
1.5 = -0.8 -----------> 0.894427191
i
1.6 = -0.641025641 ---> 0.800640769
i
1.7 = -0.529100529 ---> 0.727392967
i
1.8 = -0.446428571 ---> 0.668153104
i
1.9 = -0.383141762 ---> 0.61898446
i
2.0 = -0.333333333 ---> 0.577350268
i
3.0 = -0.125 ---------> 0.35355339
i
10 = -0.01010101 -----> 0.100503781
i
100 = -0.00010001 ----> 0.010000499
i
infinite = 0.00000 ---> 0.00000
The formula I used to plot out these numbers is
gamma = 1 / square_root( 1 - (V^2/c^2) )
This is the exact same formula I obtained from
The Starflight Handbook by Eugene Mallove and Gregory Matloff. I checked the values obtained against the values presented in the book for sublight speeds and they match, so I'm sure this is the correct formula
As you see, I've also indicated the values of
gamma squared in the middle collumn, as you can see, the values for
gamma squared are negative whenever V is greater than c. When you take the square root of a negative number the result is imaginary, but that's just fine and dandy, because role playing games are imaginary too.
One can plot out world lines in cartesian coordinates too, the vertical axis is time we can label it
t, and the horizontal axis is one dimension in space, it could be either
x,
y, or
z, it doesn't really matter. When an object is traveling a certain velocity relative to a certain frame of reference, the slope of the objects world line is its velocity. That is how much
x the object moves for a given amount of
t. In this coordinate system a distance or a light year along the
x axis is equated with a duration of a year along the
y axis, in this diagram, a beam of light moving away from the origin to the right describes a 45 degree angle with a positive slope of 1, a beam of light moving to the left from the origin has a negative slope of -1, everything in this universe that begins at the origin is bound between these two 45 degree lines. The slopes of slower than light objects moving to the right are greater than 1, the slopes of slower than light objects moving to the left are less than -1 and an object that is stationary relative to the frame of reference has an infinite slope where x has a constant value of 0. To go faster than light in this diagram means having a slope of less that 1 if moving to the right and a slope of greater than -1 if moving to the left. What this diagram demonstrates is that there is always a slower than light object whose reference point is such that a specific faster than light object appears to be moving backwards in time. A faster than light object can move freely to the right and left of the 45 degree slopes of a beam of light eminating from the origin, it can move forwards and backwards in time as a slower than light object may move in space.
Whether this is possible is up to the GM, with a tachyon beam, you can send messages backwards in time, but I imagine that assuming freedom of choice, all possible futures would be broadcasting their tachyons, and their combined emmisions would drown out any particular message sent from any particular future. You can say FTL is impossible, but then you can just go home and not play Traveller. Whether tachyons exist, I don't know, and I don't think you can find out just by manipulating numbers, but applying an equation for slower than light particles to faster than light particles seems to make logical sense.